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Group analysis and exact solutions of the time fractional Fokker–Planck equation

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  • Hashemi, M.S.

Abstract

In this paper, the Lie symmetry analysis method is extended to deal with the nonlinear time fractional Fokker–Planck (FP) equation with Riemann–Liouville derivative. The Erdélyi–Kober fractional derivative which is depending on a parameter α, is used for the reduction of FP equation. Symmetry reduction is provided and some exact analytic solutions to the time fractional FP equation are investigated by virtue of the reduction method introduced by M.C. Nucci.

Suggested Citation

  • Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    • Handle: RePEc:eee:phsmap:v:417:y:2015:i:c:p:141-149
    DOI: 10.1016/j.physa.2014.09.043
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    References listed on IDEAS

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    1. Lenzi, E.K. & Malacarne, L.C. & Mendes, R.S. & Pedron, I.T., 2003. "Anomalous diffusion, nonlinear fractional Fokker–Planck equation and solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 245-252.
    2. Huang, Qing & Zhdanov, Renat, 2014. "Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 110-118.
    3. Frank, T.D., 2004. "Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 391-408.
    4. Gang wei Wang & Tian zhou Xu & Tao Feng, 2014. "Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-6, February.
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    Cited by:

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    2. Bakhshandeh-Chamazkoti, Rohollah & Alipour, Mohsen, 2022. "Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 97-107.
    3. Biswas, Swapan & Ghosh, Uttam & Raut, Santanu, 2023. "Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.

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